An Audio Equalizer (AEQ) typically enhances, attenuates, or otherwise adjusts different frequency components in an audio signal so that the timbre of the audio signal is adapted to the hearing preference of a user to thereby improve the subjective hearing experience of the user. A parameterized digital AEQ is equivalent in principle to a high-order Infinite Impulse Response (IIR) filter, a frequency response of the high-order IIR filter is uniquely determined by the transfer function associated with the high-order IIR filter.
When the high-order IIR filter is implemented in a fixed-point way on a Digital Signal Processing (DSP) chip, that is, floating-point data is represented as fixed-point data, and hence the practical frequency response of the AEQ model may deviate from the desired theoretic design due to the quantization errors of the coefficients of the filter. In order to alleviate the influence from the quantization errors of the coefficients of the filter, it has been proposed in the prior art to decompose the high-order IIR filter into several second-order IIR filters in cascade. Mathematically the AEQ can be represented as a high-order IIR filter with the following transfer function:
                    H        AEQ            ⁡              (        z        )              =                            ∑                      k            =            0                                k            =            M                          ⁢                                  ⁢                              b            k                    ⁢                      z                          -              k                                                  1        +                              ∑                          k              =              0                                      k              =              N                                ⁢                                          ⁢                                    a              k                        ⁢                          z                              -                k                                                          ,where N≥M, and {bk} and {ak} represent the coefficients of the filter.
The equation above can be factorized into
                    H        AEQ            ⁡              (        z        )              =                  ∏                  k          =          1                          k          =          K                    ⁢                          ⁢                        H          k                ⁡                  (          z          )                      ,where K represents an integer component of (N+1)/2, which is the total number of second-order IIR filters. Hk(z) represents the k-th second-order IIR filter with the transfer function of
                    H        k            ⁡              (        z        )              =                            b                      k            ⁢                                                  ⁢            0                          +                              b                          k              ⁢                                                          ⁢              1                                ⁢                      z                          -              1                                      +                              b                          k              ⁢                                                          ⁢              2                                ⁢                      z                          -              2                                                  1        +                              a                          k              ⁢                                                          ⁢              1                                ⁢                      z                          -              1                                      +                              a                          k              ⁢                                                          ⁢              2                                ⁢                      z                          -              2                                            ,where {bki, i=0, 1, 2} and {aki, i=1, 2} represent the coefficients of the k-th second-order IIR filter which define the frequency-amplitude curve of the k-th second-order IIR filter. A set {ak1, ak2, bk0, bk1, bk2, k=1, 2, . . . , K} of the coefficients of all the second-order IIR filters defines a preset of the AEQ, which define the system frequency response-amplitude curve of the AEQ.
However for a given preset of an AEQ, there may be such an overflow occurring in fixed-point operations of each second-order IIR filter that results in nonlinear distortion, thus raising Total Harmonic Distortion (THD) of the AEQ, and consequently degrading the performance of the AEQ, especially in a High-Fidelity (HiFi) application.
In summary, given the preset of the AEQ, i.e., the coefficients of all the second-order IIR filters, in the prior art, the frequency response-amplitude curves of the second-order IIR filters are determined, so that there may be such an overflow occurring in an fixed-point output of each second-order IIR filter that results in nonlinear distortion, thus raising the THD of the AEQ, and degrading the performance of the AEQ.